Input lag with a 2.4gHz mouse + reverse acceleration with Bluetooth?

I have a Razer Basilisk X Hyperspeed Wireless gaming mouse that has both 2.4GHz and Bluetooth connections, with the ability to switch between them as needed.

2.4GHz: I discovered this problem when playing Minecraft: when I press a key on my keyboard and rapidly move my mouse, the mouse input becomes severely delayed. After I continue this delayed movement for a few seconds and suddenly stop, all of the previous physical mouse movement that was delayed--and therefore undisplayed--rushes forth suddenly in a flurry of screen movement.

After trying solutions recommended on game forums, I tried changing the mouse connection from USB 2.4GHz wireless to Bluetooth.

Bluetooth: The input lag issue vanished, but I discovered that my mouse now demonstrated what I can only call negative acceleration: When I move my mouse faster, the pointer moves slower, and vice versa. This was a clearly visible problem both in-game and on my desktop.

Any clue what's happening and how to fix it? Am I asking in the wrong place?

Edit: The input-lag exists in-game even without pressing a button. The problem does not exist when I'm just on the desktop screen.